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Course overview

Are you curious about how advanced techniques in mathematical modelling are used? Are you fascinated by the properties of black holes? Do you want to learn about insights from the latest mathematical research? Perhaps you are keen to apply this learning to a real-life situation with a placement year as part of your degree.

About mathematics at the University of Nottingham

During this MMath you will cover these topics, learning from dedicated mathematicians. Their professional research allows us to offer you a wide range of specialised modules. Our degree gives you the chance to learn more about the exciting research our academics are working on.

They are working on problems that span medical, biotechnology and food security challenges. We are conducting innovative research into stochastic epidemic modelling, thanks to experts with internationally recognised research excellence in statistics and probability.

You'll have the chance to put your knowledge into practice during the final-year dissertation. This gives you a taster what it is like to conduct your own research project under expert supervision.

Placement year

The industry placement enables you to take what you've learned and apply it to real projects in business. You will be supported by a placement tutor in securing a position and they will keep in touch during the year to see how you are getting on. They will also help you in preparing a report about your experience on your return to Nottingham for your final year. The placement year can provide you with a source of income and can even lead to a job offer before you've graduated.

What you'll study

The first-year gives you a flavour of the different areas of mathematics on offer. This helps you to decide what you enjoy and in which topics you may want to specialise. You can do this through optional modules during the later years of the degree.

Later topics include:

  • how probability and statistics are used to solve real-life problems
  • coding theory and an introduction to cryptography
  • how mathematics helps us understand population dynamics
  • how to use numerical techniques to determine the approximate solution of ordinary and partial differential equations
  • mathematical finance used for investment strategies

Your personal tutor, our student mentoring programme and small group tutorials will support your step up to university-level maths.

After graduation

The power of mathematics is about what it can do. Many graduates use the mathematical principles and techniques they have developed, for jobs in data analytics, engineering, finance, medicine and teaching. The course also provides a good foundation for further study such as a PhD.

Important to note

We are in the process of introducing exciting new learning and assessment activities for 2022 entry, to equip you with the latest knowledge and skills for a successful career using mathematics. Alongside studying essential mathematical techniques, you will have the opportunity to work with fellow students and employers on a range of activities. This will put your mathematical knowledge into practice whilst enhancing your employability.

Why choose this course?

  • Spend a year in industry to put what you have learnt into practice
  • Opportunity to network and make useful potential employer contacts
  • Peer-Assisted Study Support (PASS) run by like-minded maths students
  • Paid research internship opportunities

Entry requirements

All candidates are considered on an individual basis and we accept a broad range of qualifications. The entrance requirements below apply to 2022 entry.

UK entry requirements
A level A*AA/AAA/A*AB
Required subjects

At least A in A level mathematics. Required grades depend on whether A/AS level further mathematics is offered.

IB score IB 36; 6 in maths at Higher Level

A level

Standard offer

A*AA including A* Mathematics

or

AAA including Mathematics and Further Mathematics

or

AAA including Mathematics, plus A in AS Further Mathematics

or

A*AB including A*A in Mathematics and Further Mathematics

A level General Studies, Critical Thinking and Citizenship Studies are not accepted.

GCSEs

English 4 (C) (or equivalent)

University admissions tests

STEP/MAT/TMUA is not required but may be taken into consideration when offered.

Contextual offers

A Levels - AAB including A in Mathematics or Further Mathematics

This type of offer is given to students who meet our contextual admissions or elite athlete criteria.

Find out more about contextual offers at University of Nottingham

Alternative qualifications

In all cases we require applicants to have at least the equivalent of A level Mathematics, so we typically only accept alternative qualifications when combined with an appropriate grade in A level Mathematics.

Foundation progression options

If you don't meet our entry requirements there is the option to study the Engineering and Physical Sciences Foundation Programme. If you satisfy the progression requirements, you can progress to any of our mathematics courses.

There is a course for UK students and one for EU/international students.

Learning and assessment

How you will learn

Teaching methods

  • Computer labs
  • Lectures
  • Tutorials
  • Problem classes

How you will be assessed

You will be given a copy of our marking criteria which provides guidance on how your work is assessed. Your work will be marked in a timely manner and you will receive regular feedback.

The first year is a qualifying year but does not count towards your final degree classification. In year two the assessments will account for 20% of your final mark with years three and five accounting for 40% each. In the fifth year you will do an assessed oral presentation as part of the final year dissertation.

The year in industry will be assessed by you being required to prepare a final report and poster of your experience and taking part in a placements fair arranged by the school.

Students require 55% at the first attempt in the second year to progress on this programme. Students who do not achieve this will automatically be transferred to BSc Mathematics with a Year in Industry

Assessment methods

  • Coursework
  • Group project
  • Poster presentation
  • Research project
  • Written exam

Contact time and study hours

The majority of modules are worth 10 or 20 credits.  You will study modules totalling 120 credits in each year. As a guide one credit equates to approximately 10 hours of work. During the first year, you will typically  spend approximately:

  • 12 hours a week in lectures
  • 4 hours a week in problem classes
  • 1 hour each week in tutorials with your personal tutor
  • 1 hour a week in computing workshops across the Autumn and Spring terms
  • 1 hour each fortnight in student-led academic mentoring Peer-Assisted Study Support (PASS)

You can attend optional drop-in sessions each week up to a maximum of three hours and the remaining time will be spent in independent study.

In later years, you are likely to spend approximately 12 hours per week in lectures subject to the modules chosen.

During term time in your first year you will meet with your personal tutor every week in groups of five to six students to run through core topics. Lectures in the first two years often include at least 200 students but class sizes are much more variable in the third year subject to module selection.

Core modules are typically delivered by a mixture of Professors, Associate Professors and Lecturers, supported by PhD students in problem classes and computer lab sessions.

Year in industry

A placement year can improve your employability.

The year in industry will be supported by a named placement tutor, through a combination of telephone and/or video-conferencing calls and site visits. The year in industry will be assessed through short reflective reports on your work experience, a final report and your participation in a Mathematics with Industry Fair early in the subsequent academic year.

Modules

Due to the exciting course changes we have planned for 2022 entry, please check this page again later so that you have the most up to date information.

You will study the following core mathematics modules during your first year.

Core modules

Analytical and Computational Foundations

The idea of proof is fundamental to all mathematics. We’ll look at mathematical reasoning using techniques from logic to deal with sets, functions, sequences and series.

This module links directly with your study in Calculus and Linear Mathematics. It provides you with the foundations for the broader area of Mathematical Analysis. This includes the rigorous study of the infinite and the infinitesimal.

You will also learn the basics of computer programming. This will give you the chance to use computational algorithms to explore many of the mathematical results you’ll encounter in your core modules.

Your study will include:

  • propositional and predicate logic; set theory, countability
  • proof: direct, indirect and induction
  • sequences and infinite series (convergence and divergence)
  • limits and continuity of functions
  • programming in Python
Applied Mathematics

How can the flight-path of a spacecraft to another planet be planned? How many fish can we catch without depleting the oceans? How long would it take a lake to recover after its pollution is stopped?

The real world is often too complicated to get exact information. Instead, mathematical models can help by providing estimates. In this module, you’ll learn how to construct and analyse differential equations which model real-life applications.

Your study will include:

  • modelling with differential equations
  • kinematics and dynamics of moving bodies
  • Newton’s laws, balance of forces
  • oscillating systems, springs, simple harmonic motion
  • work, energy and motion

You'll be able to expand on these techniques later in your degree through topics such as:

  • black holes, quantum theory
  • fluid and solid mechanics
  • mathematical medicine and biology
  • mathematical finance
Calculus

How do we define calculus? How is it used in the modern world?

The concept can be explained as the mathematics of continuous change. It allows us to analyse motion and change in time and space.

You will cover techniques for differentiating, integrating and solving differential equations. You’ll learn about the theorems which prove why calculus works. We will explore the theory and how it can be applied in the real world.

Your study will include:

  • functions: limits, continuity and differentiability, rules of differentiation
  • techniques for integration, fundamental theorem of calculus
  • solution of linear and nonlinear differential equations
  • multivariate calculus, Lagrange multipliers, stationary points
  • multiple integrals, changes of variables, Jacobians

This module gives you the mathematical tools required for later modules which involve modelling with differential equations. These include:

  • mathematical physics
  • mathematical medicine and biology
  • scientific computation
Foundations of Pure Mathematics

Pure mathematics at university is typically very different to the pure mathematics you've learnt at school or college. You'll use the language of sets, functions and relations to study some very abstract mathematical ideas.

In this module, we'll develop the skills of reading and writing the language of pure mathematics. You will learn techniques to build mathematical proofs in an abstract setting.

Your study will include:

  • the language of set theory
  • relations and functions
  • rational and irrational numbers
  • modular arithmetic
  • prime factorisation

These topics will provide you with the basics you need for subsequent modules in algebra, number theory and group theory.

Linear Mathematics

Vectors, matrices and complex numbers are familiar topics from A level Mathematics and Further Mathematics. Their common feature is linearity. A linear mathematical operation is one which is compatible with addition and scaling.

As well as these topics you’ll study the concept of a vector space, which is fundamental to later study in abstract algebra. We will also investigate practical aspects, such as methods for solving linear systems of equations.

The module will give you the tools to analyse large systems of equations that arise in mathematical, statistical and computational models. For example, in areas such as:

  • fluid and solid mechanics
  • mathematical medicine and biology
  • mathematical finance

Your study will include:

  • complex numbers, vector algebra and geometry
  • matrix algebra, inverses, determinants
  • vector spaces, subspaces, bases
  • linear systems of simultaneous equations, Gaussian elimination
  • eigenvalues and eigenvectors, matrix diagonalisation
  • linear transformations, inner product spaces
Mathematical Structures

Groups, rings and fields are abstract structures which underpin many areas of mathematics. For example, addition of integers fits the structure of a group. However, by analysing the general concept of a group, our proofs are relevant to many other areas of mathematics.

You will build on your understanding of Foundations of Pure Mathematics. Together we will develop a deeper knowledge of abstract algebraic structures, particularly groups. This provides the foundation for subsequent modules in abstract algebra and number theory.

Your study will include:

  • symmetries
  • groups, cyclic groups, Lagrange’s theorem
  • rings and fields
  • integer arithmetic, Euclid’s algorithm
  • polynomial arithmetic, factorisation
Probability

What is the importance of probability in the modern world?

It allows us to assess risk when calculating insurance premiums. It can help when making investment decisions. It can be used to estimate the impact that government policy will have on climate change or the spread of disease.

We will look at the theory and practice of discrete and continuous probability. Your study will include:

  • sample spaces, events and counting problems
  • conditional probability, independence, Bayes’ theorem
  • random variables, expectation, variance
  • discrete and continuous probability distributions
  • multivariate random variables
  • sums of random variables, central limit theorem

These topics will help you prepare for later modules in:

  • probability methods
  • stochastic models
  • uncertainty quantification
  • mathematical finance
Statistics

Statistics is concerned with methods for collecting, organising, summarising, presenting and analysing data. It enables us to draw valid conclusions and make reasonable decisions based on the analysis. It can be used to answer a diverse range of questions such as:

  • Do the results of a clinical trial indicate that a new drug works?
  • Is the HS2 rail project likely to be cost-effective?
  • Should a company lend money to a customer with a given credit history?

In this module you’ll study statistical inference and learn how to analyse, interpret and report data. You’ll learn about the widely used statistical computer language R.

Your study will include:

  • exploratory data analysis
  • point estimators, confidence intervals
  • hypothesis testing
  • correlation, statistical inference
  • linear regression, chi-squared tests

These first-year topics give you the foundations for later related modules in:

  • statistical models and methods
  • data analysis and modelling
  • statistical machine learning
The above is a sample of the typical modules we offer but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. Modules (including methods of assessment) may change or be updated, or modules may be cancelled, over the duration of the course due to a number of reasons such as curriculum developments or staffing changes. Please refer to the module catalogue for information on available modules. This content was last updated on Tuesday 13 July 2021.

Choosing from a range of optional modules, you will continue to study two of the three main mathematical subject areas. You must take a minimum of 100 and maximum of 120 credits. You will also have the option to choose some modules (up to 20 credits) from outside of mathematics.

Optional modules

Algebra and Number Theory

This course will develop in more detail the fundamental concepts in algebra such as groups and rings and will provide an introduction to elementary number theory.

We will consider how general algebraic concepts can be applied in concrete situations in number theory and after a review of primes, integer factorization and module arithmetic, the focus will be on classical problems. This includes Fermat’s Little Theorem and its application to primality testing, methods of factorization, primitive roots, discrete logarithms, some classical Diophantine equations (linear and polynomial), Fibonacci numbers, and continued fractions.

Complex Functions

In this module you will learn about the theory and applications of functions of a complex variable using a method and applications approach. You will develop an understanding of the theory of complex functions and evaluate certain real integrals using your new skills.

Differential Equations and Fourier Analysis

This course is an introduction to Fourier series and integral transforms and to methods of solving some standard ordinary and partial differential equations which occur in applied mathematics and mathematical physics.

The course describes the solution of ordinary differential equations using series and introduces Fourier series and Fourier and Laplace transforms, with applications to differential equations and signal analysis. Standard examples of partial differential equations are introduced and solution using separation of variables is discussed.

Introduction to Mathematical Physics
This course develops Newtonian mechanics into the more powerful formulations due to Lagrange and Hamilton and introduces the basic structure of quantum mechanics. The course provides the foundation for a wide range of more advanced courses in mathematical physics.
Introduction to Scientific Computation

This module introduces basic techniques in numerical methods and numerical analysis which can be used to generate approximate solutions to problems that may not be amenable to analysis. Specific topics include:

  • Implementing algorithms in Matlab
  • Discussion of errors (including rounding errors)
  • Iterative methods for nonlinear equations (simple iteration, bisection, Newton, convergence)
  • Gaussian elimination, matrix factorisation, and pivoting
  • Iterative methods for linear systems, matrix norms, convergence, Jacobi, Gauss-Siedel
  • Interpolation (Lagrange polynomials, orthogonal polynomials, splines)
  • Numerical differentiation & integration (Difference formulae, Richardson extrapolation, simple and composite quadrature rules)
  • Introduction to numerical ODEs (Euler and Runge-Kutta methods, consistency, stability) 
Mathematical Analysis

In this module you will build on the foundation of knowledge gained from your core year one modules in Analytical and Computational Foundations and Calculus. You will learn to follow a rigorous approach needed to produce concrete proof of your workings.

Modelling with Differential Equations

This course aims to provide students with tools which enable them to develop and analyse linear and nonlinear mathematical models based on ordinary and partial differential equations. Furthermore, it aims to introduce students to the fundamental mathematical concepts required to model the flow of liquids and gases and to apply the resulting theory to model physical situations. 

Probability Models and Methods

This module will give you an introduction to the theory of probability and random variables, with particular attention paid to continuous random variables. Fundamental concepts relating to probability will be discussed in detail, including well-known limit theorems and the multivariate normal distribution. You will then progress onto complex topics such as transition matrices, one-dimensional random walks and absorption probabilities.

Professional Skills for Mathematicians

This module will equip you with valuable skills needed for graduate employment. You will work on two group projects based on open-ended mathematical topics agreed by your group. You will also work independently to improve your communication skills and learn how to summarise technical mathematical data for a general audience. You will be provided with some commercial and business awareness and explore how to use your mathematical sciences degree for your future career.

Statistical Models and Methods

The first part of this module provides an introduction to statistical concepts and methods and the second part introduces a wide range of techniques used in a variety of quantitative subjects. The key concepts of inference including estimation and hypothesis testing will be described as well as practical data analysis and assessment of model adequacy.

Vector Calculus

This course aims to give students a sound grounding in the application of both differential and integral calculus to vectors, and to apply vector calculus methods and separation of variables to the solution of partial differential equations. The module is an important pre-requisite for a wide range of other courses in Applied Mathematics.

Research internships

During your second year, you may want to apply to do one of the school's research internships. This involves working with an academic member of staff for 8-10 weeks over the summer.

It provides insight into the latest mathematical thinking and an opportunity to get a flavour for what a research career might be like. This is helpful if you are considering future masters or PhD study.

The above is a sample of the typical modules we offer but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. Modules (including methods of assessment) may change or be updated, or modules may be cancelled, over the duration of the course due to a number of reasons such as curriculum developments or staffing changes. Please refer to the module catalogue for information on available modules. This content was last updated on

Alongside optional mathematics modules, you will also have the option to choose some modules (up to 20 credits) from outside of mathematics.

Core modules

Choose one of the following modules worth 20 credits.

Data Analysis and Modelling

This module involves the application of probability and statistics to a variety of practical, open-ended problems, typical of those that statisticians encounter in industry and commerce. Specific projects are tackled through workshops and student-led group activities.

The real-life nature of the problems requires students to develop skills in model development and refinement, report writing and teamwork. Students will have an opportunity to apply a variety of statistical methods and knowledge learned in previous modules.

.

Mathematics Project

This module consists of a self-directed investigation of a project selected from a list of projects or, subject to prior approval of the School, from elsewhere.

Project modules are carried out in the Autumn and Spring semesters.

The project will be supervised by a member of staff and will be based on a substantial mathematical problem, an application of mathematics or investigation of an area of mathematics not previously studied by the student. The course includes training in the use of IT resources, the word-processing of mathematics and report writing.

Vocational Mathematics

This module involves the application of mathematics to a variety of practical, open-ended problems, typical of those that mathematicians encounter in industry and commerce. Specific projects are tackled through workshops and student-led group activities. The real-life nature of the problems requires students to develop skills in model development and refinement, report writing and teamwork.

Optional modules

You will select between 80 and 100 credits worth of optional modules and your choice must include at least one subject group from:

  • Applied mathematics
  • Mathematical physics
  • Pure mathematics
  • Statistics
Advanced Quantum Theory

In this module you will apply the general theory you learnt in Introduction to Mathematical Physics to more general problems. New topics will be introduced such as the quantum theory of the hydrogen atom and aspects of angular momentum such as spin.

Applied Statistical Modelling

In this module you will build on your theoretical knowledge of statistical inference by a practical implementation of the generalised linear model. You will move on to enhance your understanding of statistical methodology including the analysis of discrete and survival data. You will also be trained in the use of a high-level statistical computer program.

Classical and Quantum Dynamics

The course introduces and explores methods, concepts and paradigm models for classical and quantum mechanical dynamics exploring how classical concepts enter quantum mechanics, and how they can be used to find approximate semi-classical solutions.

In classical dynamics we discuss full integrability and basic notions of chaos in the framework of Hamiltonian systems, together with advanced methods like canonical transformations, generating functions and Hamiltonian-Jacobi theory. In quantum mechanics we recall Schrödinger's equation and introduce the semi-classical approximation. We derive the Bohr-Sommerfeld quantization conditions based on a WKB-approch to the eigenstates. We will discuss some quantum signatures of classical chaos and relate them to predictions of random-matrix theory. We will also introduce Gaussian states and coherent states and discuss their semi-classical dynamics and how it is related to the corresponding classical dynamics. An elementary introduction to complete descriptions of quantum mechanics in terms of functions on the classical phase space will be given.

Coding and Cryptography

This course provides an introduction to coding theory in particular to error-correcting codes and their uses and applications. It also provides an introduction to to cryptography, including classical mono- and polyalphabetic ciphers as well as modern public key cryptography and digital signatures, their uses and applications.

Communicating Mathematics

This course provides an opportunity for third-year students taking G100 and G103 to gain first-hand experience of being involved with providing mathematical education.

Students will work at local schools alongside practising mathematics teachers in a classroom environment and will improve their skills at communicating mathematics. Typically, each student will work with a class (or classes) for half a day a week for about sixteen weeks. Students will be given a range of responsibilities from classroom assistant to leading a self-originated mathematical activity or project. The assessment is carried out by a variety of means: on-going reflective log, contribution to reflective seminar, oral presentation and a final written report.

Data Analysis and Modelling

This module involves the application of probability and statistics to a variety of practical, open-ended problems, typical of those that statisticians encounter in industry and commerce. Specific projects are tackled through workshops and student-led group activities.

The real-life nature of the problems requires students to develop skills in model development and refinement, report writing and teamwork. Students will have an opportunity to apply a variety of statistical methods and knowledge learned in previous modules.

.

Differential Equations

This course introduces various analytical methods for the solution of ordinary and partial differential equations, focussing on asymptotic techniques and dynamical systems theory. Students taking this course will build on their understanding of differential equations covered in Modelling with Differential Equations.

Elliptic Curves

The course will start with several topics from the perspective of what can be explicitly calculated with an emphasis on applications to geometry and number theory.

Topics include:

  • basic notions of projective geometry
  • plane algebraic curves including elliptic curves
  • addition of points on elliptic curves 
  • results on the group of rational points on an elliptic curve
  • properties of elliptic curves and their applications.
Electromagnetism

The course provides an introduction to electromagnetism and the electrodynamics of charged particles. The aims of this course are:

  • to develop an appropriate mathematical model of electromagnetic phenomena that is informed by observations
  • to understand electromagnetic configurations of practical importance and to relate predictions made to everyday phenomena
  • to illustrate the use of solutions of certain canonical partial differential equations for determining electrostatic fields and electromagnetic waves in vacuum and in matter
  • to illustrate the interplay between experimental input and the development of a mathematical model, and the use of various mathematical techniques for solving relevant problems.
Fluid Dynamics
This course aims to extend previous knowledge of fluid flow by introducing the concept of viscosity and studying the fundamental governing equations for the motion of liquids and gases. Methods for solution of these equations are introduced, including exact solutions and approximate solutions valid for thin layers. A further aim is to apply the theory to model fluid dynamical problems of physical relevance.
Further Number Theory

Number theory concerns the solution of polynomial equations in whole numbers, or fractions. For example, the cubic equation x3 + y3 = z3 with x, y, z non-zero has infinitely many real solutions yet not a single solution in whole numbers.

We shall establish the basic properties of the Riemann zeta-function to find out how evenly these primes are distributed in nature. This course will present several methods to solve Diophantine equations including analytical methods using zeta-functions and Dirichlet series, theta functions and their applications to arithmetic problems, and an introduction to more general modular forms.

Game Theory
Game theory contains many branches of mathematics (and computing); the emphasis here is primarily algorithmic. The module starts with an investigation into normal-form games, including strategic dominance, Nash equilibria, and the Prisoner’s Dilemma. We look at tree-searching, including alpha-beta pruning, the ‘killer’ heuristic and its relatives. It then turns to mathematical theory of games; exploring the connection between numbers and games, including Sprague-Grundy theory and the reduction of impartial games to Nim.
Graph Theory

A graph (in the sense used in Graph Theory) consists of vertices and edges, each edge joining two vertices. Graph Theory has become increasingly important recently through its connections with computer science and its ability to model many practical situations. 

Topics covered in the course include:

  • paths and cycles
  • the resolution of Euler’s Königsberg Bridge Problem
  • Hamiltonian cycles
  • trees and forests
  • labelled trees,
  • the Prüfer correspondence
  • planar graphs
  • Demoucron et al. algorithm
  • Kruskal's algorithm
  • the Travelling Salesman's problem
  • the statement of the four-colour map theorem
  • colourings of vertices
  • chromatic polynomial
  • colourings of edges.
Group Theory

This course builds on the basic ideas of group theory. It covers a number of key results such as the simplicity of the alternating groups, the Sylow theorems (of fundamental importance in abstract group theory), and the classification of finitely generated abelian groups (required in algebraic number theory, combinatorial group theory and elsewhere). Other topics to be covered are group actions, used to prove the Sylow theorems, and series for groups, including the notion of solvable groups that will be used in Galois theory.

Linear Analysis

This module gives an introduction into some basic ideas of functional analysis with an emphasis on Hilbert spaces and operators on them.

Many concepts from linear algebra in finite dimensional vector spaces (e.g. writing a vector in terms of a basis, eigenvalues of a linear map, diagonalisation etc.) have generalisations in the setting of infinite dimensional spaces making this theory a powerful tool with many applications in pure and applied mathematics

Mathematical Finance

In this module the concepts of discrete time Markov chains are explored and used to provide an introduction to probabilistic and stochastic modelling for investment strategies, and for the pricing of financial derivatives in risky markets. You will gain well-rounded knowledge of contemporary issues which are of importance in research and applications.

Mathematical Medicine and Biology
Mathematics can be usefully applied to a wide range of applications in medicine and biology. Without assuming any prior biological knowledge, this course describes how mathematics helps us understand topics such as population dynamics, biological oscillations, pattern formation and nonlinear growth phenomena. There is considerable emphasis on model building and development.
Mathematics Project

This module consists of a self-directed investigation of a project selected from a list of projects or, subject to prior approval of the School, from elsewhere.

Project modules are carried out in the Autumn and Spring semesters.

The project will be supervised by a member of staff and will be based on a substantial mathematical problem, an application of mathematics or investigation of an area of mathematics not previously studied by the student. The course includes training in the use of IT resources, the word-processing of mathematics and report writing.

Metric and Topological Spaces

Metric space generalises the concept of distance familiar from Euclidean space. It provides a notion of continuity for functions between quite general spaces.

The module covers metric spaces, topological spaces, compactness, separation properties like Hausdorffness and normality, Urysohn’s lemma, quotient and product topologies, and connectedness. Finally, Borel sets and measurable spaces are introduced.

Multivariate Analysis

This module is concerned with the analysis of multivariate data, in which the response is a vector of random variables rather than a single random variable. A theme running through the module is that of dimension reduction. Key topics to be covered include: principal components analysis, whose purpose is to identify the main modes of variation in a multivariate dataset; modelling and inference for multivariate data, including multivariate regression data, based on the multivariate normal distribution; classification of observation vectors into sub-populations using a training sample; canonical correlation analysis, whose purpose is to identify dependencies between two or more sets of random variables. Further topics to be covered include factor analysis, methods of clustering and multidimensional scaling.

Optimisation

In this module a variety of techniques and areas of mathematical optimisation will be covered including Lagrangian methods for optimisation, simplex algorithm linear programming and dynamic programming. You’ll develop techniques for application which can be used outside the mathematical arena. 

Relativity

In this module you’ll have an introduction to Einstein’s theory of general and special relativity. The relativistic laws of mechanics will be described within a unified framework of space and time. You’ll learn how to compare other theories against this work and you’ll be able to explain new phenomena which occur in relativity.

Rings and Modules

Commutative rings and modules over them are the fundamental objects of what is often referred to as commutative algebra. Already encountered key examples of commutative rings are polynomials in one variable over a field and number rings such as the usual integers or the Gaussian integers.

There are many close parallels between these two types of rings, for example the similarities between the prime factorization of integers and the factorization of polynomials into irreducibles. In this module, these ideas are extended and generalized to cover polynomials in several variables and power series, and algebraic numbers.

Scientific Computation and Numerical Analysis

You will learn how to use numerical techniques for determining the approximate solution of ordinary and partial differential equations where a solution cannot be found through analytical methods alone. You will also cover topics in numerical linear algebra, discovering how to solve very large systems of equations and find their eigenvalues and eigenvectors using a computer.

Statistical Inference

This course is concerned with the two main theories of statistical inference, namely classical (frequentist) inference and Bayesian inference. 

Topics such as sufficiency, estimating equations, likelihood ratio tests and best-unbiased estimators are explored in detail. There is special emphasis on the exponential family of distributions, which includes many standard distributions such as the normal, Poisson, binomial and gamma.

In Bayesian inference, there are three basic ingredients: a prior distribution, a likelihood and a posterior distribution, which are linked by Bayes' theorem. Inference is based on the posterior distribution, and topics including conjugacy, vague prior knowledge, marginal and predictive inference, decision theory, normal inverse gamma inference, and categorical data are pursued.

Common concepts, such as likelihood and sufficiency, are used to link and contrast the two approaches to inference. You will gain experience of the theory and concepts underlying much contemporary research in statistical inference and methodology.

Stochastic Models

In this module you will develop your knowledge of discrete-time Markov chains by applying them to a range of stochastic models. You will be introduced to Poisson and birth-and-death processes and then you will move onto more extensive studies of epidemic models and queuing models with introductions to component and system reliability.

Vocational Mathematics

This module involves the application of mathematics to a variety of practical, open-ended problems, typical of those that mathematicians encounter in industry and commerce. Specific projects are tackled through workshops and student-led group activities. The real-life nature of the problems requires students to develop skills in model development and refinement, report writing and teamwork.

The above is a sample of the typical modules we offer but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. Modules (including methods of assessment) may change or be updated, or modules may be cancelled, over the duration of the course due to a number of reasons such as curriculum developments or staffing changes. Please refer to the module catalogue for information on available modules. This content was last updated on

You will spend this year on an industry placement.

On return to university for your final year, you will choose from a wide range of advanced optional modules. You must also write a dissertation, which accounts for one third of your fourth year. You  will specialise in one of the three main subject areas, and there is also the option to choose some modules from outside mathematics if you wish.

Core modules

Mathematics Dissertation

This module will consist of self-directed but supervised study of an appropriate area of mathematics for the whole year. A list of possible topics will be supplied by the School and students choose a topic of interest to them, The study should result in a sustained piece of work assessed by an interim report, an oral presentation and a dissertation.

 

Optional modules

You must take a minimum of 60 and maximum of 80 credits from the below.

Advanced Financial Mathematics

You will develop your knowledge and skills relevant to the mathematical modelling of investment and finance. Also, research experience will be broadened by undertaking some independent reading, computer simulations, group work and summarising the material in a project report.

Advanced Techniques for Differential Equations

The development of techniques for the study of nonlinear differential equations is a major worldwide research activity to which members of the School have made important contributions. This course will cover a number of state-of-the-art methods, namely:

  • use of green function methods in the solution of linear partial differential equations
  • characteristic methods, classification and regularization of nonlinear partial differentiation equations
  • bifurcation theory

These will be illustrated by applications in the biological and physical sciences.

Algebraic Number Theory

This module presents the fundamental features of algebraic number theory, the theory in which numbers are viewed from an algebraic point of view.

Numbers are often treated as elements of rings, fields and modules, and properties of numbers are reformulated in terms of the relevant algebraic structures. This approach leads to understanding of certain arithmetical properties of numbers (in particular, integers) from a new point of view.

 

 

Black holes

In this module you’ll systematically study black holes and their properties, including astrophysical processes, horizons and singularities. You’ll have an introduction to black hole radiation to give you an insight into problems of research interest. You’ll gain knowledge to help you begin research into general relativity.

Combinatorial Group Theory

This module is largely concerned with infinite groups, especially free groups, although their role in describing and understanding finite groups is emphasized.

Following the basic definitions of free groups and group presentations, the fundamental Nielson-Schreier Theorem is covered in some detail. Methods for manipulating group presentations, and using them to read off properties of a given group, will be covered: for example, obtaining presentations for subgroups of finite index in a given group. The interplay between presentations and standard group-theoretic construction (for example, direct products and group extensions) will also be covered. There will also be an introduction to the advanced topics of free products with amalgamation and corresponding extensions. Many of these methods may be automated and have been implemented on computers.

Computational Applied Mathematics
This course introduces computational methods for solving problems in applied mathematics. Students taking this course will develop knowledge and understanding to design, justify and implement relevant computational techniques and methodologies.
Computational Statistics

The increase in speed and memory capacity of modern computers has dramatically changed their use and applicability for complex statistical analysis. This module explores how computers allow the easy implementation of the standard, but computationally intensive, statistical methods and also explores their use in the solution of non-standard analytically intractable problems by innovative numerical methods.

The material builds on the theory of the course to cover several topics that form the basis of some current research areas in computational statistics. Particular topics to be covered include a selection from simulation methods, Markov chain Monte Carlo methods, the bootstrap and nonparametric statistics, statistical image analysis, and wavelets. You will gain experience of using a statistical package and interpreting its output.

Differential Geometry

In this module you’ll be equipped with the tools and knowledge to extend your understanding of general relativity. You’ll explore more abstract and powerful concepts using examples of curved space-times such as Lie groups and manifolds among others. You’ll have three hours of lecture per week studying this module, which may be used as example or problem classes when required.

Financial Mathematics

The first part of the module introduces no-arbitrage pricing principle and financial instruments such as forward and futures contracts, bonds and swaps, and options. The second part of the module considers the pricing and hedging of options and discrete-time discrete-space stochastic processes. The final part of the module focuses on the Black-Scholes formula for pricing European options and also introduces the Wiener process. Ito integrals and stochastic differential equations.

Introduction to Quantum Information Science

This quantum theory pathway course gives a mathematical introduction to quantum information theory. Its content builds on Introduction to Mathematical Physics with the aim of providing you with a background in quantum information science which will facilitate further independent learning and the access to current research topics.

Quantum Field Theory

In this year-long module you’ll be introduced to the study of the quantum dynamics of relativistic particles. You’ll learn about the quantum description of electrons, photons and other elementary particles leading to an understanding of the standard model of particle physics. You’ll have two hours per week of lectures studying this module.

Scientific Computing and C++
The purpose of this course is to introduce concepts of scientific programming using the object oriented language C++ for applications arising in the mathematical modelling of physical processes. Students taking this module will develop knowledge and understanding of a variety or relevant numerical techniques and how to efficiently implement them in C++.
Statistical Machine Learning

Machine Learning is a topic at the interface between statistics and computer science that concerns models that can adapt to and make predictions based on data.

This module builds on principles of statistical inference and linear regression to introduce a variety of methods of regression and classification, trade-off, and on methods to measure and compensate for overfitting. The learning approach is hands on, with students using R to tackle challenging real world machine learning problems.

Time Series and Forecasting

This module will provide a general introduction to the analysis of data that arise sequentially in time. You will discuss several commonly-occurring models, including methods for model identification for real-time series data. You will develop techniques for estimating the parameters of a model, assessing its fit and forecasting future values. You will gain experience of using a statistical package and interpreting its output.

Topics in Biomedical Mathematics

This module illustrates the applications of advanced techniques of mathematical modelling using ordinary and partial differential equations. A variety of medical and biological topics are treated bringing students close to active fields of mathematical research.

Uncertainly quantification

You will learn to apply ideas from probability and statistics and various mathematical tools in traditional areas of applied and computational mathematics involving ordinary differential equation (ODE) and partial differential equation (PDE) models.  The module will provide an introduction to a variety of techniques which are useful in UQ and will focus on a more in-depth study of selected application areas

The above is a sample of the typical modules we offer but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. Modules (including methods of assessment) may change or be updated, or modules may be cancelled, over the duration of the course due to a number of reasons such as curriculum developments or staffing changes. Please refer to the module catalogue for information on available modules. This content was last updated on

Fees and funding

UK students

£9,250
Per year

International students

To be confirmed in 2021*
Keep checking back for more information
*For full details including fees for part-time students and reduced fees during your time studying abroad or on placement (where applicable), see our fees page.

If you are a student from the EU, EEA or Switzerland starting your course in the 2022/23 academic year, you will pay international tuition fees.

This does not apply to Irish students, who will be charged tuition fees at the same rate as UK students. UK nationals living in the EU, EEA and Switzerland will also continue to be eligible for ‘home’ fee status at UK universities until 31 December 2027.

For further guidance, check our Brexit information for future students.

Additional costs

As a student on this course, you should factor some additional costs into your budget, alongside your tuition fees and living expenses.

Books

You should be able to access most of the books you’ll need through our libraries, though you may wish to purchase your own copies.

Printing

Due to our commitment to sustainability, we don’t print lecture notes but these are available digitally. You are welcome to buy print credits if you need them. It costs 4p to print one black and white page.

Industrial placement year

For the year in industry, you may be paid but you will need to factor in accommodation or travel costs. 

Equipment

Personal laptops are not compulsory as we have computer labs that are open 24 hours a day but you may want to consider one if you wish to work at home.  

Scholarships and bursaries

We offer an international orientation scholarship of £2,000 to the best international (full-time, non EU) applicants on this course.

It will be paid at most once for each year of study. If you repeat a year for any reason, the scholarship will not be paid for that repeated year. The scholarship is awarded in subsequent years to students who perform well academically (at the level of a 2:1 Hons degree or better at the first attempt). 

The scholarship will be paid in December each year provided you have:

  • completed your registration
  • been recorded as a student on a relevant course in the 1 December census
  • paid the first instalment of your fee

Alumni scholarship

The school are pleased to offer a limited number of donor-funded scholarships on a competitive basis for home MMath students joining us in September 2022, who meet the University’s Widening Participation criteria.

Each student will be awarded £1500 per year of study*. An application form for this scholarship will be available soon.

* Subject to meeting the required selection criteria.

Home students*

Over one third of our UK students receive our means-tested core bursary, worth up to £1,000 a year. Full details can be found on our financial support pages.

* A 'home' student is one who meets certain UK residence criteria. These are the same criteria as apply to eligibility for home funding from Student Finance.

International students

We offer a range of international undergraduate scholarships for high-achieving international scholars who can put their Nottingham degree to great use in their careers.

International scholarships

Careers

Mathematics is a broad and versatile subject leading to many possible careers. Our graduates are helping to shape the future in many sectors including banking and finance, business consulting and management. Other employment sectors include education, local and central government and some graduates pursue a career in mathematical research.

They have jobs such as:

  • Business analyst
  • Chartered accountant
  • Data management administrator
  • Graduate engineer
  • Graduate transport planner
  • Statistical programmer

Further study

Recent Nottingham graduates have continued their studies through masters degrees in statistics, financial mathematics and PGCEs in secondary maths. Other students have gone on to pursue a PhD in maths, statistics, computer science, fluid dynamics and quantum engineering.

Other opportunities to help your employability

Become a PASS leader in your second or third year. Teaching first-year students reinforces your own mathematical knowledge. It develops communication, organisational and time management skills which can help to enhance your CV when you start applying for jobs

The Nottingham Internship Scheme provides a range of work experience opportunities and internships throughout the year

The Nottingham Advantage Award is our free scheme to boost your employability. There are over 200 extracurricular activities to choose from

Average starting salary and career progression

83.8% of undergraduates from the School of Mathematical Sciences secured graduate level employment or further study within 15 months of graduation. The average annual salary for these graduates was £26,985.*

* HESA Graduate Outcomes 2020. The Graduate Outcomes % is derived using The Guardian University Guide methodology. The average annual salary is based on graduates working full-time within the UK.

Studying for a degree at the University of Nottingham will provide you with the type of skills and experiences that will prove invaluable in any career, whichever direction you decide to take.

Throughout your time with us, our Careers and Employability Service can work with you to improve your employability skills even further; assisting with job or course applications, searching for appropriate work experience placements and hosting events to bring you closer to a wide range of prospective employers.

Have a look at our careers page for an overview of all the employability support and opportunities that we provide to current students.

The University of Nottingham is consistently named as one of the most targeted universities by Britain’s leading graduate employers (Ranked in the top ten in The Graduate Market in 2013-2020, High Fliers Research).

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Related courses

The University has been awarded Gold for outstanding teaching and learning

Teaching Excellence Framework (TEF) 2017-18

Important information

This online prospectus has been drafted in advance of the academic year to which it applies. Every effort has been made to ensure that the information is accurate at the time of publishing, but changes (for example to course content) are likely to occur given the interval between publishing and commencement of the course. It is therefore very important to check this website for any updates before you apply for the course where there has been an interval between you reading this website and applying.